Anisotropy of localized states in an anisotropic disordered medium

We study Anderson localization of a scalar wave in an ensemble of resonant point scatterers embedded in an anisotropic background medium. For uniaxial anisotropy of moderate strength, the mobility edges and the critical exponent of the localization transition are found to be unaffected by the anisotropy provided that the determinant of the anisotropy tensor is kept equal to one upon introducing the anisotropy. Localized modes have anisotropic spatial shapes although their anisotropy is weaker than the one expected from purely geometric considerations. The modes with the longest lifetimes are found to be the most anisotropic and their anisotropy increases with the size of the disordered medium.